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when calculating the Riemann curvature tensor, you need to calculate the commutator of some vector field [tex] V [/tex], ie like this :-

[tex] [\bigtriangledown_a, \bigtriangledown_b] [/tex] = [tex] \bigtriangledown_a\bigtriangledown_b - \bigtriangledown_b\bigtriangledown_a [/tex] = [tex] V;_a_b - V;_b_a [/tex]

But why does this difference of antisymmtery give us the Riemman tensor?

thanks

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# Riemann curvature tensor derivation

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